Question

Sound waves travel from air to water. The velocity of the sound waves in air is 332 meter per second and wavelength is 2 m. If the wavelength of the sound waves is 850 cm, find its velocity in water.

Answer 1

Hint – We will start solving this question by writing down all the given information and then by using a relationship between the wavelength, frequency and wave speed, i.e., $v = f \times \lambda$, where $\left( v \right)$ is the wave speed, $f$ is the frequency and $\lambda$ is the wavelength, we will get the required result.

Complete step-by-step solution -
Formula used - $v = f \times \lambda$
We know that,
The wavelength $\left( \lambda \right)$, frequency $\left( f \right)$ and speed or velocity $\left( v \right)$of sound wave is related to each other by the relation given as follow:
$v = f \times \lambda$
i.e., wave speed or velocity = Frequency $\times$ Wavelength
Given that,
Velocity of the sound waves in air = 332 meter per second
Wavelength of the sound waves in air = 2m
Then, frequency of the sound waves in air is given by,
$v = f \times \lambda$
$\Rightarrow f = \dfrac{v}{\lambda } \\\ \Rightarrow f = \dfrac{{332}}{2} \\\ \Rightarrow f = 166Hz \\\$
Now, we have to find the velocity of this sound wave in water.
Let, ${v_w}$and ${\lambda _w}$ be the velocity and wavelength in water.
Frequency $\left( f \right)$ $= 166Hz$, as we know that frequency remains constant in both air and in water.
Also, given that, wavelength $\left( {{\lambda _w}} \right)$ of the sound wave = 850 cm =8.5 m
Now, we have the relation,
${v_w} = f \times {\lambda _w}$
$\Rightarrow {v_w} = 166 \times 8.5$
$\Rightarrow {v_w} = 1411$ $m/s$.
Hence, velocity of the sound wave in water = 1411$m/s$.

Note – The distance between two consecutive crests or troughs is called the wavelength. Unit of wavelength is meter and is denoted by lambda $\left( \lambda \right)$. Frequency is defined as the number of complete oscillations per second. Unit of frequency is hertz.